The present invention relates generally to coupling resonators and more particularly to a GT-cut quartz resonator configured so as to be in two longitudinal modes.
Conventionally the GT-cut quartz resonators are recognized as the resonator having the best frequency temperature (f-T) characteristics, i.e., the frequency change is within 1-2 PPM within the temperature range of 0.degree.-100.degree. C.
FIG. 1 shows the cut directions of a GT-cut quartz resonator. The resonator is formed from a Y plate is rotated around the X axis at .phi.=49.degree.-56.degree., then a GT-cut resonator is cut out as a plate rotated at .theta.=.+-.(40.degree.-50.degree.) within the new XZ' plane. The GT-cut quartz resonator can be resonated by coupling together two longitudinal modes respectively depending on the short side dimension W and the long side dimension L of the plate. The f-T characteristics depend on the cut angle .phi. and the side ratio r=(W/L), and excellent f-T characteristics are obtained when r=0.86-0.98.
FIG. 2 shows examples of the f-T characteristics of several types of resonators. A curve 1 indicates the f-T characteristics of the flexural resonator of tuning fork shape which is typically used for wrist watches, a curve 2 indicates the f-T characteristics of the AT-cut thickness shear resonator which is widely used for electronic instruments and the like, and a curve 3 indicates the f-T characteristics of the conventional GT-cut contour shear resonator.
Generally, it is necessary to adjust the resonance frequency of the resonator at the desired frequency to fit the intended purposes of the resonator for resonators, and of high precision in particular, it is desirable to adjust the frequency dispersion to be less than .+-.(10-20) PPM. The f-T characteristics of the GT-cut resonator, however, are oversensitive to the coupling condition between the two coupled together resonant modes, so it is very difficult to adjust the frequency without deteriorating the f-T characteristics. In the conventional large rectangular GT-cut resonator produced by mechanical techniques, the frequency is roughly adjusted by grinding the short side, and then the dimensional ratio W/L is adjusted by grinding the long side. Further the frequency is adjusted more precisely by grinding the short side, and the dimensional ratio is adjusted by grinding the long side. In this way, the desired f-T characteristics are obtained and the frequency is adjusted by gradually grinding each side. This method, however, is disadvantageous in that the work processing is difficult and takes a long time, the rate of acceptance is bad, mass production of such resonators is difficult, and the cost is expensive.